+1216 Find all the solutions to
\frac{x+4}{x+5} = \frac{x-3}{2} + \frac{x + 7}{5}
+28 we have (x+4)/(x+5)=(x-3/2)+(x+7/5)
we mutiply by 10 x+5 to get
10x+40= 5(x^2+2x-15)+2(x^2+12x+35)
10x+40= 5x^2+10x-75+2x^2+24x^2+70
0=7x^2+24x^2-45
using the formula we get
(-24+-6sqrt51)/14
(-12+-3sqrt51)/7
+130478 \(\frac{x+4}{x+5} = \frac{x-3}{2} + \frac{x + 7}{5} \)
(x + 4) / ( x + 5) = [5(x-3) + 2(x + 7)] / 10 cross-multiply
10 ( x + 4) = (x + 5) ( 7x - 1)
10x + 40 = 7x^2 + 34x - 5
7x^2 + 24x - 45 = 0
x = [ -24 +/- sqrt [ 24^2 + 45 * 4 * 7] ] / 14
x = [-24 +/- 6 sqrt 51 ] 14 = [ -12 +/- 3sqrt 51] / 7
